Field
The present application relates to apparatus and methodology for measuring properties of microporous material such as reservoir rock and core samples extracted from geologic formations.
Related Art
Permeability of a material is a macroscopic property of the material which characterizes the ease with which a fluid can be made to flow through the material by an applied pressure gradient. Thus, permeability is the fluid conductivity of the material. Porosity is the fraction of the bulk volume of the material that is occupied by voids. The total fractional volume of pores in the material can be referred to as total porosity; the fractional volume of only those pores in the material which, under given conditions, are interconnected is known as effective porosity. Only effective porosity contributes to the permeability of the material. In this application, the term “porosity” is used to describe the effective porosity of the material.
Methods for evaluating the permeability of reservoir rock using crushed fragments is described in the paper by Luffel et al. entitled “Matrix permeability measurements of gas productive shales,” SPE 26633, 1993, which reported results of a Gas Research Institute (GRI) study. These methods apply a rapid gas pressure pulse to porous sample fragments inside a container with known volume, and use transient measurements of the pressure decline rate inside the container over time to interpret the permeability of the fragments. Permeability is estimated by matching the experimental pressure curves with numerically simulated curves of pressure diffusion into multiple cylindrical fragments with fixed aspect ratio (diameter twice the height) and same size. However, no other details about assumptions in their mathematical model are disclosed. The Luffel et al. paper also presents experimental results with a very good match between permeabilities measured by pressure decay and permeabilities measured on plugs, as well as some discussion of gas slippage effects.
Several methods for measuring permeability of reservoir rock are described in the paper by Cui et al. entitled “Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications,” Geofluids, 9, 2009, pp. 208-223. These methods (including pulse decay test, pressure decay tests and canister desorption tests) can account for adsorption/desorption effects, which are taken into account as a constant correction to the diffusivity coefficient. The analysis of experimental curves is based on comparison with the exact analytical solution of a pressure diffusion equation that has constant coefficients and also involves multiple rock fragments of the same size and spherical shape. The early-time and late-time approximations to the overall solution of the pressure diffusion problem are compared. The method is based on fitting of experimental curves to the square-root of time asymptote of the analytic solution at t→0 and to the single-exponent asymptote of the analytic solution at t→∞. Based on the results of this comparison, performed using numerical modeling, the authors suggest that fitting of the late-time behavior results in better accuracy in the inferred permeability.
Methods for simultaneous measurement of stress-dependent in-situ permeability and porosity (or ISPP) are described in the paper by Cui et al., entitled “A new method to simultaneously measure in-situ permeability and porosity under reservoir conditions: implications for characterization of unconventional gas reservoirs,” SPE 138148, 2010. These methods are essentially the same method developed for rock fragments as described in SPE 26633, but applied to plug samples. In addition, the samples are subjected to tri-axial loading, to simulate reservoir conditions of stress. In this setup, one of the sample sides is connected to a reference cell with known volume. After the initial pressure differential between the gas in the sample's pore volume and the reference volume, at a particular condition of stress, is created and stabilized the valve connecting the two volumes is opened and the transient process of pressure equilibration is recorded and interpreted to infer the new porosity and permeability of the sample under the newly applied stress. The paper compares the permeability values obtained by ISPP and the conventional pulse decay method on plugs. During pressure decay gas flows through the length of a plug sample, by controlling the pressure difference at both ends of the sample, under controlled conditions of confining stress. Cui et al. report the difference in the ISPP and pulse decay permeabilities to be up to two orders of magnitude, which is explained by the intrinsic heterogeneity of samples. The study also reports considerable variation of permeability and porosity with confining stress, measured with the ISPP system. The authors indicate that the major advantage of the ISPP method compared to the traditional pressure decay method using crushed material is the ability to stress the samples. This is not possible when using fragments. The disadvantage is that increasing the size of the sample tested considerably increases the testing time. For very low permeability samples (assuming 1 inch (25.4 mm) plugs and tens of nano-Darcy or less permeability) it may take hours and be impractical for commercial laboratory services.
Several SPE papers by Lenormand et al. including i) “Advances In Measuring Porosity And Permeability From Drill Cuttings, SPE 111286, 2007; ii) “A fast and direct method of permeability measurements on drill cuttings,” SPE 77563, 2002; and iii) “Petrophysical Measurements From Drill Cuttings: An Added Value for the Reservoir Characterization Process”, SPE 88684, 2004—consider a concept analogous to pressure decay that uses the injection of viscous liquid (oil) into rock fragments (drill cuttings). SPE 77563 gives a detailed description of this concept. The method relies on the assumption that after initial liquid saturation of rock fragments at atmospheric pressure the fragments still have some of their pore volume (˜10%) uniformly filled by a trapped gas; which is trapped in the form of multiple pockets of gas isolated by liquid. During the liquid injection the residual gas volume provides compressibility that enables the flow of liquid into the particles. Both cumulative injected volume and fluid pressure in the cell are recorded at about 500 Hz sampling rate, and the permeability is interpreted based on comparisons with numerical simulations. By controlling the size of the fragments and the liquid viscosity the authors report a wide range of measureable permeabilities from 0.1 to 2000 milli-Darcy. Unfortunately, due to the high viscosity of the liquids used, compared to gas, the measurable permeability range of this system is only suitable for conventional reservoir rocks and not suitable for sub-micro Darcy unconventional reservoir rocks.
It is believed that all existing methods that characterize the permeability of rock samples using the pressure decay method employ a connected cell testing configuration. This means that after the pressure decay test is started, by opening the valve connecting the sample cell and the reference cell, this valve is maintained open throughout the test while the pressure in the sample pore volume is equilibrated to the pressure of the reference cell. In such testing, the reference and the sample cells are connected throughout the whole test, and the one pressure measurement of the reference cell is used to characterize the pressure equilibration process.
Considerable research attention has been given to non-Darcy gas flow regimes in microporous reservoir rocks. Due to the very small pore sizes in low permeability rocks, the ratio of mean free path of the gas molecules to the characteristic length scale of the flow channels becomes non-negligible. This ratio is also known as Knudsen number Kn. The higher this is, the larger the departure from Darcy regime and thus from defining the Darcy permeability of the medium. A zero value of this number (Kn=0) satisfies the Darcy regime. An overview of this effect to permeability measurements in tight shales is given, for example, in the paper by Sondergeld et al., “Petrophysical Considerations in Evaluating and Producing Shale Gas Resources,” SPE 131768, 2010.
In addition, the paper by Civan et al., “Intrinsic Shale Permeability Determined by Pressure-Pulse Measurements Using a Multiple-Mechanism Apparent-Gas-Permeability Non-Darcy Model,” SPE 135087, 2010 and the paper by Civan et al., “Shale Permeability Determined by Simultaneous Analysis of Multiple Pressure-Pulse Measurements Obtained under Different Conditions,” SPE 144253, 2011 describe pulse-decay and steady-state permeability measurements on plug samples, with elaborated consideration of variable gas compressibility, incorporating the effects of fluid density, adsorption, core porosity variation with stress, and also taking into account the effects of Knudsen flow on the apparent permeability. The latter was done using a model defined by Beskok and Karniadakis, “A model for flows in channels, pipes and ducts at micro- and nano-scales,” Journal of Microscale Thermophysical Engineering, Vol. 3, pp. 43-77, 1999.
Fathi et al., “Shale gas correction to Klinkenberg slip theory,” SPE 154977, 2012 describes the ‘double-slip’ correction to the Klinkenberg slip theory, with specific application to shale gas. The correction is based on theoretical modeling of gas flow in nano-capillaries using the Lattice Boltzmann Method (LBM). The correction modifies the Klinkenberg factor between the apparent and intrinsic fluid permeability to include a second order pressure correction and an effective capillary size. The correction relationship converges to the traditional Klinkenberg equation at smaller Kn and becomes unity when Kn is negligibly small. Two procedures are presented to estimate the intrinsic liquid permeability of samples. The first procedure is based on the estimation of the characteristic pore size h of the sample, using known porosimetry methods. With this input, the value of liquid permeability is determined from a look-up table, pre-calculated using Lattice Boltzmann Method (LBM) simulations, which provides a one-to-one relationship between h and permeability. The second procedure is based on matching the experimental values of routine pressure decay permeability on rock fragments and measured at different pore pressures, with theoretical LBM curves defining variation of apparent permeability with pore pressure. The theoretical curves are parameterized by pore pressure; the best-match effective pore size is recalculated to liquid permeability using the analytic formula k=π/ch2, where c is the geometric factor equal to 8 or 12 for cylindrical and slit pores. The idea of introducing Knudsen flow into the interpretation of pressure decay measurements pursued by Fathi has high practical value. However, the step-by-step procedures presented in his work have three critical drawbacks that make the method impractical for determining absolute permeability values: 1) the one-to-one relationship between the pore size and permeability is too strong an assumption for natural materials with heterogeneous fabric, which will not hold for combinations of pore sizes with different geometries; 2) the paper indicates that the estimation of permeability from pore size using the analytic formula and the look-up table is interchangeable in case of large channels and nearly Darcy flow; yet, the difference is several orders of magnitude; 3) the relationship between the sample's permeability and the characteristic pore size should include the porosity of the sample, otherwise the density of flow channels per unit area is not determined.
All known existing variants of the pressure decay method are directed to measuring the single permeability of the tested sample. Therefore, existing methods do not recognize the fact that many porous materials, particularly naturally formed reservoir rocks having complex fabric, incorporate wide distribution of permeabilities due to their heterogeneous nature. Furthermore, it is believed that the interpretation methods described in the literature assume isothermal conditions without explicit treatment of thermal fluctuations arising during transient gas pressure testing. However, the importance of thermal effects is known, and the American Petroleum Institute (API) document, “Recommended Practices for Core Analysis,” Recommended Practice 40, 2nd Edn., 1998, gives extensive useful recommendations on how to maintain the isothermal testing conditions during transient measurements.
Furthermore, it is believed that standard methods that characterize permeability of rock samples using the pressure decay method employ a connected cell testing configuration. This means that after the pressure decay test is started, by opening the valve connecting the sample cell and the reference cell, this valve is maintained open throughout the test while the pressure in the sample pore volume is equilibrated to the pressure of the reference cell. In such testing, the reference and the sample cells are connected throughout the whole test, and the one pressure measurement of the reference cell is used to characterize the pressure equilibration process.
The document by the American Petroleum Institute (API), “Recommended Practices for Core Analysis,” Recommended Practice 40, 2nd Edition, 1998 gives extensive useful recommendations on how to maintain the isothermal testing conditions during transient measurements. At the same time, it is believed the interpretation methods described in the open literature assume isothermal conditions without explicit treatment of thermal fluctuations arising during transient gas pressure testing.
Permeability measurements of ultra low permeability, microporous materials present challenges, particularly, in heterogeneous unconventional reservoir rocks. First, coring and core handling of heterogeneous rock samples can create extensive microcracking. The presence of these microcracks directly affects the permeability measured, and the lower the rock permeability, the larger the effect of the induced microcracks. This effect is most prevalent for laminated, low permeability, organic-rich, mudstones, where the organic to mineral contact and the interfaces associated with the laminated fabric are weak contacts that are prone to part during unloading. (This effect is less important for conventional, higher permeability rocks.)
A second challenge in measuring permeability of unconventional formations, low permeability rocks, is heterogeneity. These rocks possess intrinsic variability in texture and composition that results from geologic processes of deposition and diagenesis. As a result, these rocks exhibit a broad distribution of permeabilities. Unfortunately, conventional permeability measurements developed for homogeneous media, have focused on the evaluation of a single representative value of permeability, without accounting for the distribution of permeabilities. The resulting consequences are that the “single permeability” is ill-defined and not necessarily representative of the rock containing the distribution of permeabilities.
A third challenge to measuring permeability, if more conventional fluid flow through plug samples is used for permeability measurements, is the difficulty of flowing through the samples. It can take impractical times to detect measureable flow through samples of standard size (e.g., 1 to 1.5 inch (25.4 to 38.1 mm) in diameter and 1 to 2 inches (25.4 to 50.8 mm) in length). During these long periods of time, it may simply be impossible to not have small leaks that distort the flow measurements and thereby yield incorrect permeability inferences.
The method using crushed fragments of sample tends to be the standard method most often used for measuring permeability in ultra-low permeability rocks. However, the crushed sample fragments' measured permeabilities do not represent the mean value of the whole permeability distribution of the rock before it was crushed, unless a further calibration or correction is made to these measurements.